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binary Relation Operators

Updated March 28, 2011

Binary relation operators are symbols that establish a relationship between two quantities, usually those before and after the operator. Binary operators seldom have attributes such as subscripts or superscripts.

Standard Binary Symbols

Latex	Symbol	Description
\in	∈	element of, sideways cup with horizontal bar, opening right
\ni	∋	contains as member, reverse of \in
\leq	≤	less or equal, represented by < over = signs
\geq	≥	greater or equal, represented by > over = signs
\ll	≪	much less, represented by 2 < in a row
\gg	≫	much greater, represented by two > in a row
\prec	≺	precedes, < with both lines curving outward
\succ	≻	succeeds, reverse of \prec
\preceq	≼	precedes or equals, \prec with bottom line repeated below symbol
\succeq	≽	succeeds or equals, reverse of \preceq
\sim	∼	similar, looks like ~
\cong	≅	congruent, a \sim over =
\simeq	≃	asymptotically equal, \sym over single horizontal bar
\approx	≈	approximately equal, vertical stack of two \sym symbols
\equiv	≡	equivalent, represented by a stack of three horizontal bars
\doteq	≐	= with a dot above it
\subset	⊂	subset of, horizontal cup with opening right
\supset	⊃	superset of, horizontal cup with opening left
\subseteq	⊆	subset of or equals, \subset over single horizontal bar
\supseteq	⊇	superset of or equals, reverse of \subseteq symbol
\sqsubseteq	⊑	squared subset of or equals
\sqsupseteq	⊒	squared superset of or equals
\smile	⌣	smile without any surrounding circle
\frown	⌢	frown, without any surrounding circle
\perp	⊥	perpendicular symbol, vertical bar above and touching horizontal bar
\models	⊧	Models, represented by short vertical bar touching short = sign
\mid	∣	middle, represented by vertical \|
\parallel	∥	parallel, represented by two vertical bars in a row
\vdash	⊢	short vertical bar touching a single short horizontal bar
\Vdash	⊩	Forces, short double vertical bar touching a single short horizontal bar
\vDash	⊧	Same symbol as \models
\dashv	⊣	reverse \vdash
\propto	∝	proportional
\asymp	≍	asymptotic smile on top of and touching frown
\bowtie	⋈	normal subgroup of, bow tie shape or right -pointing triangle on left touching left-pointing triangle on right
\sqsubset	⊏	square subset of, squared \subset
\sqsupset	⊐	square superset of, squared version of \supset
\Join	⋈	same symbol as \bowtie
\pm	±	plus or minus
\mp	∓	minus or plus
\times	×	times multiplication sign
\cdot	·	dot multiplication symbol
\circ	∘	ring operator
\bigcirc	◯	large circle
\div	÷	divide, represented by dots above and below horizontal bar
\diamond	⋄	diamond operator
\ast	∗	asterisk operator
\star	☆	white star
\cap	∩	cap, intersection
\cup	∪	cup, union
\sqcap	⊓	square cap, intersection
\sqcup	⊔	square cup, union
\wedge	∧	wedge, logical AND
\vee	∨	V operator, logical OR
\triangleleft	◃	left pointing triangle
\triangleright	▹	Right pointing triangle
\bigtriangleup	△	wide up triangle
\bigtriangledown	▽	wide down triangle
\oplus	⊕	circled plus
\ominus	⊖	circled minus
\otimes	⊗	circled times sign
\oslash	⊘	circled slash
\odot	⊙	circled dot operator
\bullet	•	bullet
\dagger	†	daggar
\ddagger	‡	double daggar
\setminus	\ ∖	Set Minus
\uplus	⊎	multiset union
\wr	≀	wreath product
\amalg	⨿	Amalgamation or Co-product
\lhd	⊲	Normal subgroup of
\rhd	⊳	Contains as normal subgroup
\unlhd	⊴	Normal subgroup of or equals to
\unrhd	⊵	Contains as normal subgoup or equal to
\dotplus	∔	dot plus
\centerdot	⋅	centered dot
\ltimes	⋉	Left normal factor semi-direct product
\rtimes	⋊	Right normal factor semi-direct product
\leftthreetimes	⋋	Left semi-direct product
\rightthreetimes	⋌	Right semi-direct product
\circleddash	⊖	circled minus
\smallsetminus	∖	Same as \setminus
\barwedge	⊼	NAND
\curlywedge	⋏	curly logical AND
\curlyvee	⋎	curly logical OR
\veebar	⊻	XOR
\intercal	⊺	intercalate
\Cup	⋓	double union
\Cap	⋒	double intersection
\circledast	⊛	circled asterisk operator
\circledcirc	⊚	circled ring operator
\boxminus	⊟	squared minus
\boxtimes	⊠	squared times
\boxdot	⊡	squared dot operator
\boxplus	⊞	squared plus
\divideontimes	⋇	division times
\And	&	AND

Advanced AMS Binary Symbols

\leqslant	⩽	less than or slanted equals to
\geqslant	⩾	greater than or slanted equals
\eqslantless	⪕	slanted equal to or less than
\eqslantgtr	⪖	slanted equal to or greater than
\lesssim	≲	less or quivalent
\gtrsim	≳	greater or quivalent
\lessapprox	⪅	less than or approximate
\gtrapprox	⪆	greater or approximate
\approxeq	≅	approximately equal
\lessdot	⋖	less with dot
\gtrdot	⋗	greater with dot
\lll	⋘	very much less
\ggg	⋙	very much greater than
\lessgtr	≶	less or greater
\gtrless	≷	greater or less than
\lesseqgtr	⋚	less than equals to or greater than
\gtreqless	⋛	Greater than equal to or less than
\lesseqqgtr	⪋	less than above equals to above greater than
\gtreqqless	⪌	greater than above equals to above less than
\doteqdot	≑	geometrically equal
\eqcirc	≖	equals with circle in middle
\circeq	⊜	circled equals
\fallingdotseq	≒	Approximately equal to or the image of
\risingdotseq	≓	Image of or approximately equal to
\triangleq	≜	delta equals
\backsim	∽	reverse similar symbol
\thicksim	∼	same as \sim (similar) symbol
\backsimeq	⋍	reverse similar or equals
\thickapprox	≈	thick approximately equal
\preccurlyeq	≼	precedes or equals
\succcurlyeq	≽	succeeds or equals
\curlyeqprec	⋞	equal or precedes
\curlyeqsucc	⋟	equal or succeeds
\precsim	≾	precedes or equivalent
\succsim	≿	succeeds or equivalent
\precapprox	⪷	precedes above almost equals to
\succapprox	⪸	succeeds above almost equals to
\subseteqq	⫅	subset of above equals
\supseteqq	⫆	superset of above equals
\Subset	⋐	double subset
\Supset	⋑	double superset
\vartriangleleft	⊲	normal subgroup of
\vartriangleright	⊳	contains as normal subgroup of
\trianglelefteq	⊴	normal subgroup of or equal
\trianglerighteq	⊵	contains as normal subgroup or equal
\VDash	⊫	double vertical bar double right turnstile
\Vdash	⊩	Forces symbol
\Vvdash	⊪	Triple vertical bar, right turnstile
\Bumpeq	≎	geometrically equivalent
\between	≬	between
\pitchfork	⋔	pitchfork
\backepsilon	϶	reverse Greek epsilon symbol
\blacktriangleleft	◂	black small left-pointing triangle
\blacktriangleright	▸	black small right-pointing triangle
\therefore	∴	therefore
\because	∵	because

AMS binary symbols negated

\ne	≠	not equal
\notin	∉	not an element of
\nless	≮	not less
\ngtr	≯	not greater
\nleq	≰	neither less or equal
\ngeq	≱	neither greater or equal
\lneq	⪇	less than and single line not equal to
\gneq	⪈	greater than and single line not equal to
\lneqq	≨	Less than but not equal to
\gneqq	≩	greater but not equal
\lnsim	⋦	less but not equivalent
\gnsim	⋧	greater but not equivalent to
\lnapprox	⪉	less and not approximately equal
\gnapprox	⪊	greater and not approximately equal to
\nprec	⊀	does not precede
\nsucc	⊁	does not succeeds
\npreceq	⋠	does not precede or equal
\nsucceq	⋡	does not succeed or equal
\precneqq	⪵	Precedes above not equal
\succneqq	⪶	succeeds above not equal to
\precnsim	⋨	precedes but not equivalent to
\succnsim	⋩	succeeds but not equivalent
\precnapprox	⪹	precedes above not almost equal to
\succnapprox	⪺	succeeds above not approximately equal to
\nsim	≁	not similar
\ncong	≇	not congruent
\nmid	∤	not divide
\nparallel	∦	not parallel
\nvdash	⊬	does not prove
\nvDash	⊭	not true
\nVdash	⊮	not force
\nVDash	⊯	negated double vertical bar double right turnstile
\ntriangleleft	⋪	not normal subgroup of
\ntriangleright	⋫	does not contain as normal subgroup
\ntrianglelefteq	⋬	not normal subgoup of or equal
\ntrianglerighteq	⋭	does not contain as normal subgroup or equal
\nsubseteq	⊈	neither subset of nor equal
\nsupseteq	⊉	neither superset of nor equal
\subsetneq	⊊	subset of with not equal
\supsetneq	⊋	superset with not equal
\subsetneqq	⫋	subset of above not equal to
\supsetneqq	⫌	superset of above not equal to

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